bioelectric function of the nerve cell

7/29/2019 Bioelectric Function of the Nerve Cell

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BIOELECTRIC FUNCTION OF THE NERVE CELL

The membrane voltage (transmembrane

voltage) (Vm) of an excitable cell is

defined as the potential at the inner

surface (i) relative to that at the outer

(o) surface of the membrane, i.e. Vm =

(i) - (o). This definition is independent

of the cause of the potential, and whetherthe membrane voltage is constant,

periodic, or nonperiodic in behavior.

Fluctuations in the membrane potential

may be classified according to their

character in many different ways. Figure2.7 shows the classification for nerve cells

developed by Theodore Holmes Bullock

(1959). According to Bullock, these

transmembrane potentials may be

resolved into a resting potential and

potential changes due to activity. The

latter may be classified into three different

types:

1. Pacemaker potentials: the intrinsic

activity of the cell which occurs

without external excitation.


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2. Transducer potentials across the

membrane, due to external events.

These includegeneratorpotentials caused by receptors

orsynaptic potentialchanges arising

at synapses. Both subtypes can be

inhibitory or excitatory.

3. As a consequence of transducerpotentials, further response will arise.

If the magnitude does not exceed the

threshold, the response will

be nonpropagating (electrotonic). If

the response is great enough, a nerveimpulse (action potential impulse) will

be produced which obeys the all-or-

nothing law (see below) and proceeds

unattenuated along the axon or fiber.


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Fig. 2.7. Transmembrane potentials

according to Theodore H. Bullock.

2.5 EXCITABILITY OF NERVE CELL

If a nerve cell is stimulated, the

transmembrane voltage necessarily

changes. The stimulation may be

excitatory (i.e., depolarizing;

characterized by a change of the

potential inside the cell relative to the

outside in the positive direction, and

hence by a decrease in the normally

negative resting voltage) or


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inhibitory (i.e., hyperpolarizing,

characterized by a change in the

potential inside the cell relative to theoutside in the negative direction, and

hence by an increase in the magnitude

of the membrane voltage).

After stimulation the membrane voltage

returns to its original resting value.

If the membrane stimulus is insufficient to

cause the transmembrane potential to

reach the threshold, then the membrane

will not activate. The response of the

membrane to this kind of stimulus isessentially passive. Notable research on

membrane behavior

undersubthresholdconditions has been

performed by Lorente de N (1947) and

Davis and Lorente de N (1947).If the excitatory stimulus is strong

enough, the transmembrane potential

reaches the threshold, and the membrane

produces a characteristic electric impulse,

the nerve impulse. This potential response


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follows a characteristic form regardless of

the strength of the transthreshold

stimulus. It is said that the actionimpulse of an activated membrane follows

an all-or-nothinglaw. An inhibitory

stimulus increases the amount of

concurrent excitatory stimulus necessary

for achieving the threshold (see Figure

2.8). (The electric recording of the nerve

impulse is called the action potential. If

the nerve impulse is recorded

magnetically, it may be called an action

current. The terminology is further

explicated in Section 2.8 and in Figure2.11, below.)


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Fig. 2.8. (A) Experimental

arrangement for measuring the

response of the membrane potential

(B) to inhibitory (1) and excitatory (2,

3, 4) stimuli (C). The current stimulus(2), while excitatory is, however,

subthreshold, and only a passive

response is seen. For the excitatory

level (3), threshold is marginally

reached; the membrane is sometimes


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activated (3b), whereas at other times

only a local response (3a) is seen. For

a stimulus (4), which is clearlytransthreshold, a nerve impulse is

invariably initiated.

2.6 THE GENERATION OF THE ACTIVATION

The mechanism of the activation is

discussed in detail in Chapter 4 inconnection with the Hodgkin-Huxley

membrane model. Here the generation of

the activation is discussed only in general

terms.

The concentration of sodium ions (Na+

) isabout 10 times higher outside the

membrane than inside, whereas the

concentration of the potassium (K+) ions

is about 30 times higher inside as

compared to outside. When the membrane

is stimulated so that the transmembrane

potential rises about 20 mV and reaches

the threshold - that is, when the

membrane voltage changes from -70 mV

to about -50 mV (these are illustrative and

common numerical values) - the sodium


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and potassium ionic permeabilities of the

membrane change. The sodium ion

permeability increases very rapidly atfirst, allowing sodium ions to flow from

outside to inside, making the inside more

positive. The inside reaches a potential of

about +20 mV. After that, the more

slowly increasing potassium ion

permeability allows potassium ions to

flow from inside to outside, thus returning

the intracellular potential to its resting

value. The maximum excursion of the

membrane voltage during activation is

about 100 mV; the duration of the nerveimpulse is around 1 ms, as illustrated in

Figure 2.9. While at rest, following

activation, the Na-K pump restores the ion

concentrations inside and outside the

membrane to their original values.


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Fig. 2.9. Nerve impulse recorded from

a cat motoneuron following a

transthreshold stimulus. The stimulusartifact may be seen at t= 0.

2.7 CONCEPTS ASSOCIATED WITH THE ACTIVATION PROCESS

Some basic concepts associated with the

activation process are briefly defined in

this section. Whether an excitatory cell is

activated depends largely on the strength

and duration of the stimulus. The

membrane potential may reach the

threshold by a short, strong stimulus or a

longer, weaker stimulus. The curve


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illustrating this dependence is called

thestrength-duration curve; a typical

relationship between these variables isillustrated in Figure 2.10. The smallest

current adequate to initiate activation is

called the rheobasic currentorrheobase.

Theoretically, the rheobasic current needs

an infinite duration to trigger activation.

The time needed to excite the cell with

twice rheobase current is called chronaxy.

Accommodation and habituation denote

the adaptation of the cell to a continuing

or repetitive stimulus. This is

characterized by a rise in the excitationthreshold.Facilitation denotes an increase

in the excitability of the cell;

correspondingly, there is a decrease in the

threshold.Latency denotes the delay

between two events. In the presentcontext, it refers to the time between

application of a stimulus pulse and the

beginning of the activation. Once

activation has been initiated, the

membrane is insensitive to new stimuli,


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no matter how large the magnitude. This

phase is called the absolute refractory

period. Near the end of the activationimpulse, the cell may be activated, but

only with a stimulus stronger than normal.

This phase is called the relative refractory

period.

The activation process encompasses

certain specifics such as currents,

potentials, conductivities, concentrations,

ion flows, and so on. The term action

impulse describes the whole process.

When activation occurs in a nerve cell, it

is called a nerve impulse;correspondingly, in a muscle cell, it is

called a muscle impulse.

The bioelectric measurements focus on

the electric potentialdifference across the

membrane; thus the electric measurementof the action impulse is called the action

potentialthat describes the behavior of

the membrane potential during the

activation. Consequently, we speak, for

instance, ofexcitatory postsynaptic


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potentials (EPSP) and inhibitory

postsynaptic potentials (IPSP).

In biomagnetic measurements, it is theelectric currentthat is the source of the

magnetic field. Therefore, it is logical to

use the term action currentto refer to the

source of the biomagnetic signal during

the action impulse. These terms are

further illustrated in Figure 2.11.


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Fig. 2.10. (A) The response of the

membrane to various stimuli of

changing strength (B), the strength-

duration curve. The level of current

strength which will just elicit


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activation after a very long stimulus is

called rheobase. The minimum time

required for a stimulus pulse twice therheobase in strength to trigger

activation is called chronaxy. (For

simplicity, here, threshold is shown to

be independent on stimulus duration.)

Fig. 2.11. Clarification of theterminology used in connection with

the action impulse:

A) The source of the action impulse

may be nerve or muscle cell.

Correspondingly it is called a nerve

impulse or a muscle impulse.


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B) The electric quantity measured

from the action impulse may be

potential or current. Correspondinglythe recording is called an action

potential or an action current.

2.8 CONDUCTION OF THE NERVE IMPULSE IN AN AXON

Ludvig Hermann (1872, 1905) correctly

proposed that the activation propagates inan axon as an unattenuated nerve impulse.

He suggested that the potential difference

between excited and unexcited regions of

an axon would cause small currents, now

called local circuit currents, to flowbetween them in such a direction that they

stimulate the unexcited region.

Although excitatory inputs may be seen in

the dendrites and/or soma, activation

originates normally only in the soma.

Activation in the form of the nerve

impulse (action potential) is first seen in

the root of the axon - the initial segment

of the axon, often called the axon hillock.

From there it propagates along the axon.

If excitation is initiated artificially


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somewhere along the axon, propagation

then takes place in both directions from

the stimulus site. The conduction velocitydepends on the electric properties and the

geometry of the axon.

An important physical property of the

membrane is the change in sodium

conductance due to activation. The higher

the maximum value achieved by the

sodium conductance, the higher the

maximum value of the sodium ion current

and the higher the rate of change in the

membrane voltage. The result is a higher

gradient of voltage, increased localcurrents, faster excitation, and increased

conduction velocity. The decrease in the

threshold potential facilitates the

triggering of the activation process.

The capacitance of the membrane per unitlength determines the amount of charge

required to achieve a certain potential and

therefore affects the time needed to reach

the threshold. Large capacitance values,


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with other parameters remaining the

same, mean a slower conduction velocity.

The velocity also depends on theresistivity of the medium inside and

outside the membrane since these also

affect the depolarization time constant.

The smaller the resistance, the smaller the

time constant and the faster the

conduction velocity. The temperature

greatly affects the time constant of the

sodium conductance; a decrease in

temperature decreases the conduction

velocity.

The above effects are reflected in anexpression derived by Muler and Markin

(1978) using an idealized nonlinear ionic

current function. For the velocity of the

propagating nerve impulse in

unmyelinated axon, they obtained(2.1)

where v = velocity of the nerve impulse [m/s]

iNa max = maximum sodium current per unit length [A/m]

Vth = threshold voltage [V]

ri = axial resistance per unit length [/m]

cm = membrane capacitance per unit length [F/m]


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A myelinated axon (surrounded by the

myelin sheath) can produce a nerve

impulse only at the nodes of Ranvier. Inthese axons the nerve impulse propagates

from one node to another, as illustrated in

Figure 2.12. Such a propagation is

calledsaltatory conduction (saltare, "to

dance" in Latin).

The membrane capacitance per unit length

of a myelinated axon is much smaller than

in an unmyelinated axon. Therefore, the

myelin sheath increases the conduction

velocity. The resistance of the axoplasmper unit length is inversely proportional to

the cross-sectional area of the axon and

thus to the square of the diameter. The

membrane capacitance per unit length is

directly proportional to the diameter.

Because the time constant formed from

the product controls the nodal

transmembrane potential, it is reasonable

to suppose that the velocity would be

inversely proportional to the time

constant. On this basis the conduction


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velocity of the myelinated axon should be

directly proportional to the diameter of

the axon. This is confirmed in Figure2.13, which shows the conduction

velocity in mammalian myelinated axons

as linearly dependent on the diameter. The

conduction velocity in myelinated axon

has the approximate value shown:v = 6d (2.2)

where v = velocity [m/s]

d= axon diameter [m]

Fig. 2.12. Conduction of a nerveimpulse in a nerve axon.

(A) continuous conduction in an

unmyelinated axon;

(B) saltatory conduction in a

myelinated axon.


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Fig. 2.13. Experimentally determined

conduction velocity of a nerveimpulse in a mammalian myelinated

axon as a function of the diameter.

(Adapted from Ruch and Patton,

1982.)

REFERENCES

bioelectric function of the nerve cell

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